# Find the length of the line segment determined by the given pair of points. P(2,-2) and Q(-1,2)

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The Pythagorean Theorem which applies to right triangles states that:

a and b are the lengths of the legs while c is the length of the hypotenuse.

In the Cartesian plane they are:

The points are have coordinates

This means

are the coordinates of the first point

and are the coordinates of the second

So in the problem:

which are the coordinates of P

which are the coordinates of P

We substitute this to the Pythagorean theorem

The triangle that will be formed has a very common Pythagorean triple which is (3,4,5).

The length of the hypotenuse (or any length of a side) cannot be less than or equal to 0 so it cannot be -5.

Therefore the length of the line segment when you connect the two points is 5.

The Pythagorean Theorem which applies to right triangles states that:

a and b are the lengths of the legs while c is the length of the hypotenuse.

In the Cartesian plane they are:

The points are have coordinates

This means

are the coordinates of the first point

and are the coordinates of the second

So in the problem:

which are the coordinates of P

which are the coordinates of P

We substitute this to the Pythagorean theorem

The triangle that will be formed has a very common Pythagorean triple which is (3,4,5).

The length of the hypotenuse (or any length of a side) cannot be less than or equal to 0 so it cannot be -5.

Therefore the length of the line segment when you connect the two points is 5.